Ch05 Lecture Force and Motion I - Middle East Technical ...

Chapter 5

Force and Motion I

http://en.wikipedia.org/wiki/File:Skaters_showing_newtons_third_law.svg

5 Force and Motion I

25 October 2018 2 PHY101 Physics I © Dr.Cem Özdoğan


5-2 Newtonian Mechanics

Mechanics of Particle Motion 1. Newtonian Mechanics: Study of relation between force and

acceleration of a body. • Sir Isaac Newton (1642-1727)

• Three laws relating force and motion.

• Valid for a wide range of speed and scale of

interacting bodies. Valid for our daily life.

• Newtonian Mechanics does not hold good for all situations!

2. Special Theory of Relativity

• Albert Einstein (1879-1955)

• Holds for all speed including close to speed of light.

• Replaces Newtonian Mechanics for very large speed.

3. Quantum Mechanics

• Replaces Newtonian Mechanics for interacting bodies on the

scale of atomic structure.

• A force is a “push”or “pull” acting on a object and causes acceleration.


5-3 Newton’s First Law

• A body at rest tends to remain at rest & a body in motion at a constant

velocity will tend to maintain the velocity.

If no force acts on a body, the body’s velocity cannot change; that is,

the body cannot accelerate.

Before Newtonian mechanics; Some influence (force) was thought necessary

to keep a body moving. The “natural state” of objects was at rest.


5-4 Force

• A force is measured by the acceleration it produces.

• Forces have both magnitudes and directions.

• Principle of superposition of forces:

• A net force has the same impact as a single force with identical

magnitude and direction.

netF : Sum of forces acting on a body (net force, resultant force)

1 Newton = 1 kg.m/s² (SI)


5-5 Mass

• What is mass?

• Mass is the property of an object that measures how hard it is to change

its motion. Body’s resistance to a change in velocity.

• It is an intrinsic characteristic of a body. It is not the same as weight,

density, size etc.

• The mass of a body is the characteristic that relates a force on the body

to the resulting acceleration.

• The ratio of the masses of two bodies is equal to

the inverse of the ratio of their accelerations when

the same force is applied to both. Example Apply an 8.0 N force to various bodies:

Mass: 1kg → acceleration: 8 m/s2

Mass: 2kg → acceleration: 4 m/s2

Mass: 0.5kg → acceleration: 16 m/s2

Acceleration: 2 m/s2 → mass: 4 kg


5-6 Newton’s Second Law

Identify the body in question, and only include forces that act on that

body! Separate the problem axes (they are independent):


5-6 Newton’s Second Law; Drawing a free-body diagram (FBD)

• In a free-body diagram, the only body shown

is the one for which we are summing forces.

• Each force on the body is drawn as a vector

arrow with its tail on the body.

• A coordinate system is usually included.

• Acceleration is NEVER part of a free body

diagram - only forces on a body are present.

If the net force on a body is zero:

• Its acceleration is zero

• The forces and the body are in equilibrium

• But there may still be forces!


Example:

Fig. 5-3 In three situations, forces act on a

puck that moves along an x axis.



Example:



5-7 Some Particular Forces

1) The Gravitational Force:

-Fg = m(-g) or Fg = mg.

A gravitational force on a body is a certain type of pull that is directed

toward a second body.

2) Weight:

The weight, W, of a body is equal to the magnitude Fg of the gravitational

force on the body.

W = mg (weight),

or

CAUTION: A body’s weight is not its mass!


3) Normal Force: (Normal means perpendicular)

For any vertical acceleration ay of the table and block.

When a body presses against a surface, the

surface (even a seemingly rigid one)

deforms and pushes on the body with a

normal force, FN, that is perpendicular to

the surface.

Fig. 5-7 (a) A block resting on a table experiences a

normal force perpendicular to the tabletop. (b) The

free-body diagram for the block.

In the figure: Newton’s second law says

for a positive-upward y axis:

(Fnet, y= may), as:



4) Friction: • If we either slide or attempt to slide a body over a

surface, the motion is resisted by a bonding between the

body and the surface.

• The force f is either called frictional force or simply

friction. Directed along the surface, opposite to the

direction of intended motion.

• Sometimes, to simplify a stiuation, friction is assumed to be negligible.

(So the surface is frictionless.)

5) Tension

Fig. 5-9 (a) The cord, pulled taut, is under tension. If its mass is negligible,

the cord pulls on the body and the hand with force T, even if the cord runs

around a massless, frictionless pulley as in (b) and (c).

• When a cord is attached to a

body and pulled taut, the

cord pulls on the body with a

force T directed away from

the body and along the cord.



5-8 Newton’s Third Law: : Symmetry in Forces

• When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction and collinear.

• The forces between two interacting bodies are

called a third-law force pair.

http://en.wikipedia.org/wiki/File:Skaters_showing_newtons_third_law.svg


5-8 Newton’s Third Law

2) Compare the magnitudes of the acceleration you experience, aA, to the magnitude of

the acceleration of the spacecraft, aS, while you are pushing:

1. aA = aS

2. aA > aS

3. aA < aS

1) Suppose you are an astronaut in outer space giving a brief push to a

spacecraft whose mass is bigger than your own. Compare the magnitude of the

force you exert on the spacecraft, FS, to the magnitude of the force exerted by

the spacecraft on you, FA, while you are pushing:

1. FA = FS

2. FA > FS

3. FA < FS

correct

correct

a=F/m

(F same lower mass gives larger a)

Third Law!


5-9 Applying Newton’s Laws


Example : Cord accelerates block up a ramp

Using Newton’s Second

Law, we have :

which gives:

The positive result indicates

that the box accelerates

up the plane.



Example : Reading a force graph

Answer: ax=-2 m/s2



Example: Forces within an elevator cab

• The reading is equal to the magnitude of

the normal force on the passenger from the

scale.

• We can use Newton’s Second Law only in

an inertial frame. If the cab accelerates,

then it is not an inertial frame. So we

choose the ground to be our inertial frame

and make any measure of the passenger’s

acceleration relative to it.



Example (Continued): Forces within an elevator cab



Example: Acceleration of block pushing on block

Answer: ax=-2 m/s2,

FBA=12 N



Example:

(OpenStax 4.6) Calculate the tension in the wire supporting the 70.0-kg

tightrope walker shown in Figure.


(Serway 5.4) A traffic light weighing 122 N hangs from a cable tied to two

other cables fastened to a support as in Figure. The upper cables make angles of

37.0° and 53.0° with the horizontal. These upper cables are not as strong as the

vertical cable and will break if the tension in them exceeds 100 N. Does the

traffic light remain hanging in this situation, or will one of the cables break?

Example:


(Serway 5.9) When two objects of unequal mass are hung vertically over a

frictionless pulley of negligible mass as in Figure, the arrangement is called an

Atwood machine. The device is sometimes used in the laboratory to calculate

the value of g. Determine the magnitude of the acceleration of the two objects

and the tension in the lightweight cord.

Example:


5 Solved Problems

1. In Figure, let the mass of the block be 8.5 kg and the

angle be 30°. Find (a) the tension in the cord and (b) the

normal force acting on the block. (c) If the cord is cut,

find the magnitude of the resulting acceleration of the

block.


5 Solved Problems

2. A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves

forward a distance of 65 cm (with respect to the road) while being brought to rest

by an inflated air bag. What magnitude of force (assumed constant) acts on the

passenger's upper torso, which has a mass of 41 kg?


5 Solved Problems

3.A car that weighs 1.30x104 N is initially moving at 40 km/h when the brakes are

applied and the car is brought to a stop in 15 m. Assuming the force that stops the car

is constant, find (a) the magnitude of that force and (b) the time required for the

change in speed. If the initial speed is doubled, and the car experiences the same

force during the braking, by what factors are (c) the stopping distance and (d) the

stopping time multiplied?


5 Solved Problems

3. (Continued) A car that weighs 1.30x104 N is initially moving at 40 km/h when the

brakes are applied and the car is brought to a stop in 15 m. Assuming the force that

stops the car is constant, find (a) the magnitude of that force and (b) the time required

for the change in speed. If the initial speed is doubled, and the car experiences the

same force during the braking, by what factors are (c) the stopping distance and (d)

the stopping time multiplied?.


5 Solved Problems

4. An elevator cab and its load have a combined mass of 1600 kg. Find the tension in

the supporting cable when the cab, originally moving downward at 12 m/s, is

brought to rest with constant acceleration in a distance of 42 m.


5 Solved Problems

5. Figure shows a box (mass m1=3.0 kg) on a

frictionless plane inclined at angle θ1 =30o . The

box is connected via a cord of negligible mass to

a box (mass m2=2.0 kg) on a frictionless plane

inclined at angle θ2 =60o. The pulley is

frictionless and has negligible mass. What is the

tension in the cord?


5 Solved Problems

5. (Continued) Figure shows a box (mass m1=3.0

kg) on a frictionless plane inclined at angle θ1

=30o . The box is connected via a cord of

negligible mass to a box (mass m2=2.0 kg) on a

frictionless plane inclined at angle θ2 =60o. The

pulley is frictionless and has negligible mass.

What is the tension in the cord?


5 Summary

Newtonian Mechanics

Forces are pushes or pulls

Forces cause acceleration

Force

Vector quantities

1 N = 1 kg m/s2

Net force is the sum of all

forces on a body

Inertial Reference Frames

Frames in which Newtonian

mechanics holds

Newton's First Law

If there is no net force on a

body, the body remains at rest if

it is initially at rest, or moves in

a straight line at constant speed

if it is in motion.


5 Summary

Mass

The characteristic that relates

the body's acceleration to the

net force

Scalar quantity

Newton's Second Law

Free-body diagram represents

the forces on one object

Newton's Third Law

Law of force-pairs

If there is a force by B on C,

then there is a force by C

on B:

Some Particular Forces

Weight:

Normal force from a surface

Friction along a surface

Tension in a cord

Eq. (5-1)

Eq. (5-12)

Eq. (5-15)


Additional Materials

5 Force and Motion I


5-4 Force; Inertial Reference Frames

(a) The path of a puck sliding from the

north pole as seen from a stationary

point in space. Earth rotates to the

east. (b) The path of the puck as seen

from the ground.

•If a puck is sent sliding along a short strip of frictionless ice—the puck’s

motion obeys Newton’s laws as observed from the Earth’s surface.

• If the puck is sent sliding along a long ice strip extending from the north

pole, and if it is viewed from a point on the Earth’s surface, the puck’s path

is not a simple straight line.

•The apparent deflection is not caused by a force, but by the fact that we see

the puck from a rotating frame. In this situation, the ground is a

noninertial frame.


Force; The Four Basics Forces


5-1_6 Newton's First and Second Laws

5.01 Identify that a force is a

vector quantity and thus has

both magnitude and direction

and also components.

5.02 Given two or more forces

acting on the same particle, add

the forces as vectors to get the

net force.

5.03 Identify Newton's first and

second laws of motion.

5.04 Identify inertial reference

frames.

5.05 Sketch a free-body diagram

for an object, showing the

object as a particle and drawing

the forces acting on it as vectors

anchored to the particle.

5.06 Apply the relationship

between net force on an object,

its mass, and the produced

acceleration.

5.07 Identify that only external

forces on an object can cause

the object to accelerate.

Learning Objectives



5.08 Determine the magnitude and

direction of gravitational force on a

mass, for a given free-fall

acceleration.

5.09 Identify that weight is the

magnitude of the net force required

to prevent a body from falling

freely, measured by the frame of

ground.

5.10 Identify that a scale gives an

object’s weight when the

measurement is done in an inertial

frame but not in an accelerating

frame, where it gives an apparent

weight.

5.11 Determine the magnitude and

direction of the normal force on

an object when the object is

pressed or pulled onto a surface.

5.12 Identify that the force parallel

to the surface is a frictional force

that appears when the object

slides or attempts to slide.

5.13 Identify that a tension force is

said to pull at both ends of a cord

(or a cord-like object) when the

cord is taut.

Learning Objectives


5-8 Applying Newton's Laws

Learning Objectives 5.14 Identify Newton's third law

of motion and third-law of force

pairs.

5.15 For an object that moves

vertically or on a horizontal or

inclined plane, apply Newton's

second law to a free-body

diagram of the object.

5.16 For an arrangement where a

system of several objects moves

rigidly together, draw a free-

body diagram and apply

Newton's second law for the

individual objects and also for

the system taken as a composite

object.

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